Each vowel in the word TRAJECTORIES is changed to the second letter immediately following it in the English alphabetical order, a…

Question

Each vowel in the word TRAJECTORIES is changed to the second letter immediately following it in the English alphabetical order, and each consonant is changed to the second letter immediately preceding it in the English alphabetical order. How many letters will appear exactly twice in the new group of letters thus formed?

1. A. Two
2. B. One
3. C. Three
4. D. Four (Correct answer)

Correct Answer

Option D — Four

Detailed Solution & Explanation

The correct answer is Four.

Key Points

• Transform TRAJECTORIES letter by letter — vowels move +2 forward, consonants −2 backward:
  • T→R, R→P, A→C, J→H, E→G, C→A, T→R, O→Q, R→P, I→K, E→G, S→Q
• The new group is R P C H G A R Q P K G Q.
• Now count how many letters appear exactly twice:
  • R (×2), P (×2), G (×2), Q (×2) — four letters
  • C, H, A and K each appear once
• The answer is Four.

Additional Information

• Write the transformed sequence out in full before counting. The question asks about the *new* group, and attempting to count frequencies while transforming is where the error occurs.
• Note the two rules move in opposite directions — vowels forward, consonants backward. Applying one direction to both is the commonest slip.
• The vowels in TRAJECTORIES are A, E, O, I, E; everything else is a consonant. Identifying them first makes the transformation mechanical.
• Read the final question precisely: "exactly twice" excludes any letter appearing once or three times. Counting all repeated letters, or all distinct letters, gives different answers — both of which appear among the options.